Arithmetic of curves on moduli of local systems

@article{Whang2018ArithmeticOC,
  title={Arithmetic of curves on moduli of local systems},
  author={Junho Peter Whang},
  journal={arXiv: Number Theory},
  year={2018}
}
  • J. Whang
  • Published 13 March 2018
  • Mathematics
  • arXiv: Number Theory
We study the Diophantine geometry of algebraic curves on relative moduli of special linear rank two local systems over surfaces. We prove that the set of integral points on any nondegenerately embedded algebraic curve can be effectively determined. Under natural hypotheses on the embedding in relation to mapping class group dynamics of the moduli space, the set of all imaginary quadratic integral points on the curve is shown to be finite. Our ingredients include a boundedness result for… 

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